How to make a wave that follows empty?
To make just one wave uncheck the Cyclic option on the wave modifier.

Then just find the proper offset so that when the empty moves across the object the wave occurs.







EDIT

Another option I can think of (not knowing what you are after ultimately) is not using a wave modifier but a displace modifier, and using the empty to control the texture. Animating the strenght as the empty goes across the sphere can give a nice result: